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We focus on the structure of the set of noncentral idempotents whose role is similar to one of central idempotents. We introduce the concept of quasi-Abelian rings which unit-regular rings satisfy. We first observe that the class of quasi-Abelian rings is seated between Abelian and direct finiteness. It is proved that a regular ring is directly finite if and only if it is quasi-Abelian. It is also shown that quasi-Abelian property is not left-right symmetric, but left-right symmetric when a given ring has an involution. Quasi-Abelian property is shown to do not pass to polynomial rings, comparing with Abelian property passing to polynomial rings.
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참고문헌 (7)
참고문헌 신청
G. Ehrlich / 1968 / Unit-regular rings / Portugal. Math. 27:209~212
K. R. Goodearl / 1979 / Von Neumann Regular Rings / Pitman
S. U. Hwang / 2006 / Structure and topological conditions of NI rings / J. Algebra 302(1):186~199
N. Jacobson / 1950 / Some remarks on one-sided inverses / Proc. Amer. Math. Soc. 1:352~355
N. K. Kim / 2000 / Armendariz rings and reduced rings / J. Algebra 223(2):477~488
K. R. Goodearl / 1979 / Von Neumann Regular Rings / Pitman
S. U. Hwang / 2006 / Structure and topological conditions of NI rings / J. Algebra 302(1):186~199
N. Jacobson / 1950 / Some remarks on one-sided inverses / Proc. Amer. Math. Soc. 1:352~355
N. K. Kim / 2000 / Armendariz rings and reduced rings / J. Algebra 223(2):477~488
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